We study cascades on a two-layer multiplex network, with asymmetric feedback that depends on the coupling strength between the layers. Based on an analytical branching process approximation, we calculate the systemic risk measured by the final fraction of failed nodes on a reference layer. The results are compared with the case of a single layer network that is an aggregated representation of the two layers. We find that systemic risk in the twolayer network is smaller than in the aggregated one only if the coupling strength between the two layers is small. Above a critical coupling strength, systemic risk is increased because of the mutual amplification of cascades in the two layers. We even observe sharp phase transitions in the cascade size that are less pronounced on the aggregated layer. Our insights can be applied to a scenario where firms decide whether they want to split their business into a less risky core business and a more risky subsidiary business. In most cases, this may lead to a drastic increase of systemic risk, which is underestimated in an aggregated approach.

When a new product or technology is introduced, potential consumers can learn its quality by trying it, at a risk, or by letting others try it and free-riding on the information that they generate. We propose a dynamic game to study the adoption of technologies of uncertain value, when agents are connected by a network and a monopolist seller chooses a profit-maximizing policy. Consumers with low degree (few friends) have incentives to adopt early, while consumers with high degree have incentives to free ride. The seller can induce high-degree consumers to adopt early by offering referral incentives -rewards to early adopters whose friends buy in the second period. Referral incentives thus lead to a 'double-threshold strategy' by which low and high-degree agents adopt the product early while middle-degree agents wait. We show that referral incentives are optimal on certain networks while inter-temporal price discrimination is optimal on others.

We model the production of complex goods in a large supply network. Firms source several essential inputs through relationships with other firms. Relationships may fail, and given this idosyncratic risk, firms multisource inputs and make costly investments to make relationships with suppliers stronger (less likely to fail). We find that aggregate production is discontinuous in the strength of these relationships. This has stark implications for equilibrium outcomes. We give conditions under which the supply network is endogenously fragile, so that arbitrarily small negative shocks to relationship strength lead to a large, discontinuous drop in aggregate output.

The efficacy of positive end-expiratory pressure (PEEP) in treating intraoperative hypoxemia during one-lung ventilation (OLV) remains in question given conflicting results of prior studies. This study aims to (1) evaluate the efficacy of PEEP during OLV, (2) assess the utility of preoperative predictors of response to PEEP, and (3) explore optimal intraoperative settings that would maximize the effects of PEEP on oxygenation. Forty-one thoracic surgery patients from a single tertiary care university center were prospectively enrolled in this observational study. After induction of general anesthesia, a double-lumen endotracheal tube was fiberoptically positioned and OLV initiated. Intraoperatively, PEEP = 5 and 10 cm H(2)O were sequentially applied to the ventilated lung during OLV. Arterial oxygenation, cardiovascular performance parameters, and proposed perioperative variables that could predict or enhance response to PEEP were analysed. T-test and χ(2) tests were utilized for continuous and categorical variables, respectively. Multivariate analyses were carried out using a classification tree model of binary recursive partitioning. PEEP improved arterial oxygenation by ≥20% in 29% of patients (n = 12) and failed to do so in 71% (n = 29); however, no cardiovascular impact was noted. Among the proposed clinical predictors, only intraoperative tidal volume per kilogram differed significantly between responders to PEEP and non-responders (mean 6.6 vs. 5.7 ml/kg, P = 0.013); no preoperative variable predicted response to PEEP. A multivariate analysis did not yield a clinically significant model for predicting PEEP responsiveness. PEEP improved oxygenation in a subset of patients; larger, although still protective tidal volumes favored a positive response to PEEP. No preoperative variables, however, could be identified as reliable predictors for PEEP responders.

We model the production of complex goods in a large supply network. Each firm sources several essential inputs through relationships with other firms. Individual supply relationships are at risk of idiosyncratic failure, which threatens to disrupt production. To protect against this, firms multisource inputs and strategically invest to make relationships stronger, trading off the cost of investment against the benefits of increased robustness. A supply network is called fragile if aggregate output is very sensitive to small aggregate shocks. We show that supply networks of intermediate productivity are fragile in equilibrium, even though this is always inefficient. The endogenous configuration of supply networks provides a new channel for the powerful amplification of shocks. (JEL D21, G31, L14)